At what temperature does the $r.m.s.$ speed of air molecules become double that at $N.T.P.$?

If the $rms$ speed of hydrogen gas is equal to the $rms$ speed of oxygen gas at $47^{\circ}C$,find the temperature of the hydrogen gas in $K$.

For a given gas,the velocities of $5$ molecules are $2, 3, 4, 5,$ and $6$. What is the $rms$ velocity?

$A$ container is divided into two equal halves by a diathermic partition. Two different ideal gases are filled in the left $(L)$ and right $(R)$ parts. The $rms$ speed of the molecules in the $L$ part is equal to the average speed of the molecules in the $R$ part. Find the ratio of the mass of a molecule in the $L$ part to the mass of a molecule in the $R$ part.

At a given temperature,the root mean square velocities of oxygen and hydrogen molecules are in the ratio:

An $HCl$ molecule has rotational,translational,and vibrational motions. If the $rms$ velocity of $HCl$ molecules in its gaseous phase is $\bar{v}$,$m$ is its mass,and $k_B$ is the Boltzmann constant,then its temperature will be: